The Lexicon of Knotology

Knotting Concepts & Explorations
21

Bights, loops, eyes and Turns - another family of ‘Aunt Sallies’

TURN() is a base generic term. It is a partial term, requiring the additional definition of ‘by how much’ so the term should always be used in combination with the amount (which should include its units (NB when the units are not included then the units are taken to be hR)). The amount could be stated in degrees, radians or ‘half revolutions’ (hR), so TURN(1 hR) is a turn back on itself, while a TURN(3 hR) would have been called a ‘Round Turn’. Turns may be made around another object (or self) or not, and may be made incorporating an end, or not.

TURN() incorporates the sub terms BIGHT, LOOP and WRAP, and LOOP includes the sub term EYE

 [b]T.BIGHT[/b] is a TURN(1 hR) without ends and without a contained object.  It also used to refer to a mid portion of cord (i.e. without ends), but is now taken to mean a mid section plus a TURN(1 hR).  In doing so, it creates a new doubled cord END which is generally used to create a KNOT mid-line. (Utilising Dan's definition a hard-folded, "doubled" structure (w/o [s]much[/s] any attention to whether its ends ever cross)

 [b]T.WRAP[/b] is a TURN(2 hR) with or without an end and around an object (often self).  WRAP is often compounded to create a series of turns adjacently around the object or self.

 [b]T.LOOP[/b] is a TURN(1 hR) with or without an end, with or without an object and does not form a new double stranded cord.  A loop is open and is generally formed to contain an object or to fix an object (or self) to.

       [b]LOOP.EYE[/b] is a LOOP made tightly around an object ? ?
22

Using this schema, both LOOP and BIGHT are TURN(1). By adding another distinction to TURN(1) we should be able to dispense with these two specific terms. The LOOP is Object(indeterminate) Double End(NO), while the BIGHT is Object(NO) Double End(YES). If we use the convention of 0 for NO, 1 for YES and blank for indeterminate, we can add these distinctions to the TURN() description.

TURN( Amount of Turn , Object included , Double End formed )[/size][/color]

BIGHT then is TURN( 1 , 0 , 1) - i.e. 1hR, no object, double end formed.
While LOOP is TURN( 1 , , 0) - i.e. 1hR, object not specified, no double end.

Alternatively, we could make more use of the Object term by using it to denote anything, nothing, self or fixture.
Anything (, ,) - as the term suggests , the loop can contain something if you want, as in the bowline, you can make it around an object or clip into it or not - your choice.
Nothing (,0,) – the loop must be clear - apart from decorative, I can’t think why you would use this.
Self (,s,)-- the loop goes around some other part of the cord.
Fixture(,f,) – as in a hitch or a loop around an anchor or other solid object etc.

This only leaves the question of with or sans ‘an end’ - from this follows the question of ‘how far from an end?’. Obviosuly, the end cannot be incorporated, otherwise it is not a loop, and ‘how far from an end?’ is surely no more relevant than ‘how long is a piece of string?’ - so lets try working without the ‘with / without end’ criterion.

We can compile all the present terms and attempt to rationalise them or we can essentially dispose of them and attempt to create a rational terminology to see if we can work with it. Personally I do not care what the OED defines a loop or a bight as and do not believe that we should limit ourselves by these existing definitions - after all we are only on this thread because we know the mess these present definitions are in.

Can this sort of logic take us forward or is this too far too fast?

Derek

23

I’ll try to look at these ideas more closely later today. Out of curiosity, are you making use of any of Peter Suber’s work? I haven’t studied his notation in detail yet, but it might help prevent “reinventing the wheel” if his ideas are useful. Might make our work go faster, especially if he has already dealt with any notational “snags” and issues which we haven’t yet encountered.

Here’s his “cheat sheet” for his notation: http://www.earlham.edu/~peters/knotting/notate-dict.htm.

Dave

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Nodist Colony - Exclusive community of knotters…

25

Hi Dave,

No I have not used any of Peters terms for three reasons.

First, his work sits nicely alone as a markup language or shorthand to describe the moves taken in making a knot.

Second, Peters goal was to create a tying language and not to rationalise our lexicon. Consequently he uses numerous terms such as ‘fore’ and ‘aft’ and ‘clockwise’ in his descriptions. Peter did not seem to be concerned about a logical structure for the language he drew his terms from. Some of his notation may match where this lexicon ends up, but I believe we should go for clarity and unambiguity rather than be driven by what has gone before.

And third, although his work is seminal, it has not caught on, probably because his terminology is so cryptic. Modern XML’s are rigid in their structure and their terminology, but far more descriptive in the terms used. Understanding GP(SP, LH), GP(RP, RH), *2 ML(RP)=LP.1, CO(RP, SP), PN(LP.1:HP), *3 RV(E.RP, LP.1.D-U), *4 MV(SP^:L, RP^:R) as the method to tie the OH is more arduous even than trying to read a KM file. I think he is right when he says “Unfortunately, these virtues are in tension. We can have one or the other, probably not both.” His work is foundational and doubtless will become the starting point for the next generation markup language that can be machine read.

Derek

PS - at that nodist colony - would string vests be compulsory ?

26

It would be a no strings attached nodist colony… :wink:

27

Hrmm – without attachment or binding, it wouldn’t be Nodism, so it couldn’t be a Nodist colony ! !

Come on - keep up there Cap’n Billy

28

On the contrary my friend…you don’t want to go in there all knotted up…with no strings attached there is nothing to do but get bent, hitched, looped, bound or knotted…me thinks I am way ahead of you… :smiley:

29

One thing that comes to mind is that a notation such as TURN( 1 , 0 , 1) might lead to confusion because it’s easy to forget what each parameter means.

Then I started thinking about the word “Turn.” We’re familiar with it from such things as “Round Turns,” but it strikes me that “Turn” doesn’t really describe the action that we’re trying to describe. You defined a “Turn” in terms of half revolutions, which I believe hits the nail on the head. Instead of thinking of ways to distinguish between Loops and Wraps and so on, what if we refer to such things in terms of Revolutions, such as “0.5 Revolutions,” “1 Revolution,” “1.5 Revs,” and so on. This will simplify the terminology because we have a single term (Revolutions or Revs) which is modified by the number of Revs to make. For example, in traditional terminology we would say, “Make a Round Turn around the post,” but in Nodology we might say, “Make 1.5 Revolutions around the post.”

“Bight” is another traditional term that we’re familiar with, but which isn’t very descriptive in itself. You pointed out that when making a Bight, “it creates a new doubled cord END,” which is a good description. I would suggest that a better and more descriptive term for “Bight” would be something like “Doubled_End.” For a simplistic example, in traditional terminology we would say, “Make a Loop, then push a Bight through it,” but in Nodology we might say, “Make a Revolution and push a Doubled_End through it.” Or “Make a 1 Rev and push a Doubled_End through it.”

Thoughts?

Dave

30

edit (2/18/2010): The ideas below are out-of-date. The new proposed terms are listed and defined in the Nodeology wiki at http://nodeology.pbworks.com/Bindings-Terms.

Playing around with some more ideas:

N.TAIL_END = The end of the N.CORDAGE which is used in tying an N.KNOT. Traditionally referred to as the Working End, Bitter End, or Running End.

Reasoning: TAIL_END seems more descriptive and familiar than Working End, Bitter End, or Running End.  This term is easily grasped and remembered because people understand such things as "the tail end of the line" or "the tail end of the lecture," etc.

N.EXIT_PART = The part of the N.CORDAGE which exits the N.KNOT and ends at the N.TAIL_END.

Reasoning: This terminology creates a matching pair with N.ENTRY_PART.

N.ENTRY_PART = The part of the N.CORDAGE which enters the N.KNOT at the opposite end from the N.EXIT_PART (“opposite” in the sense that one part of a rope enters into a knot, and another part of the rope exits from the knot). Traditionally referred to as the Standing Part.

Reasoning: "Standing Part" is not very intuitive.  ENTRY_PART and EXIT_PART create a matching pair of terms which should help make their meanings more descriptive and intuitive.  I also like MAIN_PART as a replacement for Standing Part, but imagine if we tie a series of knots along a rope (working towards the end of the rope).  On each successive knot, where's "the Standing Part" or "the Main Part of the rope"?  Is it the part of the rope which is beyond our first knot in the series?  ENTRY_PART is perhaps more intuitive because it describes the section of rope which comes immediately before ("entering into") the knot which we're currently tying.

N.LOOP = The oval-shaped length of N.CORDAGE which remains after certain N.KNOTS are tied (e.g. Bowline). Useful for throwing over a post, or for clipping onto with an attachment such as a carabiner, and so on. Traditionally referred to as a Loop or an Eye.

Reasoning: "Eye" is sometimes used for the oval-shaped length of cordage, but "Eye" gives the impression of smallness (for example, no land creature has an eye which is as big as the loop that we usually form with a Bowline).  "Loop" has at least two meanings in traditional terminology, but in Nodology we're replacing one of those meanings with something like N.TURN(2 hR) or N.REVOLUTION(1).  Therefore, N.LOOP is intuitive and descriptive and unique.

I’m starting to think that my terminology of “1 REVOLUTION” should probably be “N.REVOLUTION(1)” instead. In addition, perhaps N.REVOLUTION(1, CROSS_OVER) and N.REVOLUTION(1, CROSS_UNDER) can replace the traditional “Overhand Loop” and “Underhand Loop,” respectively. “CROSS_OVER” means that the N.TAIL_END crosses over the N.ENTRY_PART (from the perspective of the knot-tyer). “CROSS_UNDER” means that the N.TAIL_END crosses under the N.ENTRY_PART (from the perspective of the knot-tyer).

This new terminology seems to work fairly well, even though we still have a number of gaps to be filled. For example:

“To tie a Bowline, form an N.REVOLUTION(1, CROSS_OVER) in the air and push the N.TAIL_END through the hole in the N.REVOLUTION to create an N.LOOP, then bring the N.TAIL_END around the N.ENTRY_PART and back through the hole in the N.REVOLUTION. For safety, leave a fairly long N.EXIT_PART.”

One obvious gap to be filled is how to specify the direction in which the N.TAIL_END is pushed through the N.REV in the above example.

Thoughts?

Dave

edit: Added a clarification of “opposite” in the definition of N.ENTRY_PART.

edit (2/18/2010): The ideas above are out-of-date. The new proposed terms are listed and defined in the Nodeology wiki at http://nodeology.pbworks.com/Bindings-Terms.

31

When describing how to tie a knot, another useful term might be:

N.STARTING_ORIENTATION(orientation, location of the N.TAIL_END) = Describes the orientation of the N.CORDAGE (from the perspective of the knot-tyer) before the N.KNOT is tied. For the parameters, the valid combinations are:

    Orientation   Location of the N.TAIL_END
    -----------   --------------------------
    VERTICAL      END_DOWN (i.e. the N.TAIL_END is at the bottom) or END_UP
    HORIZONTAL    END_LEFT or END_RIGHT
    DIAGONAL      END_NW or END_NE or END_SW or END_SE

So N.STARTING_ORIENTATION(VERTICAL, END_DOWN) means that before you begin tying the knot, you would hold the rope so that it’s vertical with the TAIL_END at the bottom. This helps ensure that your actions are properly in sync with the knot-tying instructions.

Perhaps this is jumping too far ahead, but I wanted to get some thoughts down before I forget them.

Dave

32

More ideas for consideration:

N.JOIN_KNOT = The category of N.KNOTS which are used for tying two or more N.TAIL_ENDS of N.CORDAGE together (whether from the same N.CORDAGE or from different N.CORDAGES). Traditionally referred to as a Bend.

N.LOOP_KNOT = The category of N.KNOTS which result in one or more N.LOOPS. If two N.LOOPS are formed (e.g. the Spanish Bowline) then the N.KNOT is an N.LOOP_KNOT(2), and so on.

N.TETHER_KNOT = The category of N.KNOTS which are used for tying around an object and which conform to the shape of the object. “Tether” means “To fasten to a fixed object.” Traditionally referred to as a Hitch. An animal can be tethered to a post using a Bowline, for example, but the Bowline would still be referred to as an N.LOOP_KNOT because it is not conforming to the shape of the post.

Dave

33

edit (2/18/2010): The ideas below are out-of-date. The new proposed terms are listed and defined in the Nodeology wiki at http://nodeology.pbworks.com/Bindings-Terms.

Attempting to compile all of the ideas so far…

Nodology – The field and study of bindings made in cordage.

N.Cordage – Any material capable of being manipulated into N.Bindings. Includes rope, chain, cable, cord, string, thread, braid, plait, wool, leather thong, ribbon, and so on.

N.Binding – The result of manipulating cordage components into shapes that are capable of translating forces from one part to another. Includes knots, splices, whippings, and so on.

[b]N.B.Splice[/b] -- Creating a force transferring connection by knotting the cordage and/or sub parts of the cordage on and through itself.

[b]N.B.Whipping[/b] -- Effecting the transfer of force by wrapping a smaller diameter cord tightly around the outside of the cordage being bound.

[b]N.B.Stitching[/b] -- N.B.Whipping but involving both the inside and the outside of the cordage being bound.

[b]N.B.Weaving[/b] -- Creating sheets of flexible fabric by interweaving or plaiting numerous strands of cordage.

[b]N.B.Netting[/b] -- Creating sheets of widely spaced cords by knotting strands of cordage.

[b]N.B.Knot[/b] -- Creating a force transferring connection by creating 3 dimensional contact structures on the surface of the cord only.


  Parts of an N.B.Knot (see the reasoning for these terms in an earlier post):

    [b]N.B.K.Tail_End[/b] -- The end of the N.Cordage which is used in tying an N.B.Knot.  Traditionally referred to as the Working End, Bitter End, or Running End.

    [b]N.B.K.Exit_Part[/b] -- The part of the N.Cordage which exits the N.B.Knot and ends at the N.B.K.Tail_End.

    [b]N.B.K.Entry_Part[/b] -- The part of the N.Cordage which enters the N.B.Knot at the opposite end from the N.B.K.Exit_Part ("opposite" in the sense that one part of a rope enters into a knot, and another part of the rope exits from the knot).  Traditionally referred to as the Standing Part.

    [b]N.B.K.Loop[/b] -- The oval-shaped length of N.Cordage which remains after certain N.B.Knots are tied (e.g. Bowlines).  Useful for throwing over a post, or for clipping onto with an attachment such as a carabiner, and so on.  Traditionally referred to as a Loop or an Eye.

    [b]N.B.K.Doubled_End[/b] -- When a length of N.Cordage is folded over ("doubled") so that a new "end" is created, this is an N.B.K.Doubled_End.  Traditionally referred to as a Bight.

    [b]N.B.K.Turn(amount of turn, object included, double end formed)[/b] -- Taking a length of N.Cordage around an object (or simply around the air).  "Amount of turn" specifies how many times around, in half-revolutions (e.g. 1hR).  "Object included" specifies whether or not the N.Cordage goes around an object.  Valid values are: " " (anything), "0" (nothing), "s" (self), or "f" (fixture, i.e. an anchor or other solid object).  "Double end formed" specifies whether or not an N.B.K.Doubled_End is formed.  N.B.K.Turn(1, 0, 1) is traditionally referred to as a Bight.  N.B.K.Turn(1,  , 0) is traditionally referred to as a Loop.

    [b]N.B.K.Revolution(number, crossing)[/b] -- Alternative idea for N.B.K.Turn.  Taking a length of N.Cordage around an object (or simply around the air).  "Number" specifies how many times around.  "Crossing" specifies whether the N.Cordage crosses over or under itself.  Valid values are:  "Cross_Over" or "Cross_Under" or "None."  When tied in the air, N.B.K.Revolution(0.5, None) is traditionally referred to as a Bight.  When tied in the air, N.B.K.Revolution(1, Cross_Under) is traditionally referred to as an Underhand Loop.  When tied around an object, N.B.K.Revolution(1.5, None) is traditionally referred to as a Round Turn.


  Types of N.B.Knots:

    [b]N.B.K.Join_Knot[/b] -- An N.B.Knot which is used for tying two or more N.B.K.Tail_Ends together (whether from the same N.Cordage or from different N.Cordages).  Traditionally referred to as a Bend.

    [b]N.B.K.Loop_Knot(optional number of loops)[/b] -- An N.B.Knot which results in one or more N.B.K.Loops.  If two N.B.K.Loops are formed (e.g. the Spanish Bowline) then the N.B.Knot is an N.B.K.Loop_Knot(2), and so on.

    [b]N.B.K.Tether_Knot[/b] -- An N.B.Knot which is used for tying a length of N.Cordage around an object and which conforms to the shape of the object.  "Tether" means "To fasten to a fixed object."  Traditionally referred to as a Hitch.  An animal can be tethered to a post using a Bowline, for example, but the Bowline would still be referred to as an N.B.K.Loop_Knot because it doesn't conform to the shape of the post.

    [b]N.B.K.Hitch_Knot[/b] -- An alternative idea for N.B.K.Tether_Knot.

Looking over this list, “N.B.K.” seems a bit cumbersome. Perhaps all of the above terms should simply be prefixed with “N.” to indicate that they are Nodology terms?

As Derek pointed out, this is a start for a new and clearer and unambiguous set of knotting terms. So how do these terms (and their definitions) sound so far? What improvements can be made?

Some more terms which have been used in this forum, to perhaps incorporate into Nodology somehow:

sling
collar
nub
nip
lead
capsize
jam
slipped
noose (i.e. an Overhand slip knot but loaded the opposite way)
half hitch
lashing
“front view” and “back view” of a knot (I don’t know if it’s possible to come up with a useful definition of these two terms)

Dave

edit (2/18/2010): The ideas above are out-of-date. The new proposed terms are listed and defined in the Nodeology wiki at http://nodeology.pbworks.com/Bindings-Terms.

34

Dave,

I really like the ideas you have been expressing and I must say that you have been delightfully prolific so far. I would like to suggest, however, that we should go back a pace or two and ask ourselves - what is nodology? What are the component parts of nodology? How could we rationally divide and then sub-divide if necessary to have a reasonable shot at getting to grip with some defining terms? I suggest the following:

Nodology: The field and study of structures made in N.cordage
N.Cordage: Any material capable of being manipulated by hand or machine into N.tyings, N.weavings or N.bindings
N.tyings: the resulting transfer of force(s) from one place to another using N.cordage when joining it to something else, whether N.cordage or a solid object,
N.weavings: the resulting fabric formed when passing N.cordage over or under one or more N.cordages, whether those N.cordages are the same or a different piece,
N.bindings: the resulting covering of another N.cordage(s) or object(s) using friction

Then, we could go on to subdivide thus:
N.T.Knot:
N.T.Hitch:
N.T.Bend:
N.T.Loop:
N.W.Flatmat:
N.W.Splice:
N.W.Ball:
N.W.Cylinder:
N.B.Finishing (Whipping):
N.B.Covering (Serving):
N.B.Lashing (Seizing):

I feel sure that there are more but what do you think of those potential sub-divisions?

SR

35

Hi SR,

I agree with you about the importance of finding good subdivisions for classifying the terms in Nodology.

In Derek’s model, everything that can be made by manipulating cordage would fall under the Binding subdivision. Your model has Tyings, Weavings, and Bindings as separate subdivisions (at the same level). As we work with these ideas then we’ll be able to determine which model is a better fit, or perhaps a different model will emerge as the best fit.

Some questions for you:

  1. Under the Tyings subdivision you have Knot, Hitch, Bend, and Loop. Is there a reason for saying that Hitches, Bends, and Loops are not Knots?

  2. “Hitch” is a traditional term which might be descriptive enough to be a good fit in the new Nodology lexicon, but “Bend” is a traditional term which isn’t very descriptive. Also, if “Loop” is the name for the category of knots which include Bowlines, Alpine Butterflys, etc., then what would be the term for the part of those knots which forms a “loop”? Are there better and more descriptive terms for the categories of “Bend” and “Loop”?

Dave

36

I find this discussion fascinating - it must be what the developers of esperanto went through and I have a feeling that this will go the same way. Great idea but ignores the simple fact that language, no matter how imprecise or even bizaarre, develops at its own speed through common usage. I will always use salt on food never sodium chloride so as long as Nodologists see themselves in a similar way to other specialist groups eg scientists this stands a chance but only amongst the cognoscenti of consenting adults. I reckon 6 weeks to 3 months and the next novelty will surface but we can all enjoy watching while it lasts.

Barry
:smiley:

37

I have been looking over The Braider & some of the other publications by AG Schakkee and John Turner. Yes, a bit on the complicated side for the average person. But I do like how the authors proceed in the publications in the actual design and mathematical processes, and the terms they use pretty much consistently throughout all of their publications. I am not quite sure if this would be a way to go, or not. But I think that using the terms they have used would be a great start. For example, to describe the term Turns, instead they use Half Cycle. I realize that they use that term in the building of a grid for the final outcome of a knot. Of course these terms would most likely be more associated with the scientific and mathematical nomenclature. But I feel that this would be a grounded start for all of us to be on the same page so that it would become much easier to share amongst colleagues. Well just a thought and it may not be of any use, but just another idea to play with. I figure if we don’t have to reinvent the wheel, the more time we can save.

Brian…

38

True, most of us say “salt” instead of “sodium chloride.” Yet “sodium chloride” is a useful term among certain groups of people (e.g. chemists). In the same way, most knotters will probably continue to use traditional terms, but the Nodology terminology will allow us to use more precise and unambiguous language when needed.

Quite true, although there’s always the possibility that a wider audience might begin using the new terminology if it’s useful. But as Derek stated in the original post, “For the sake of starting somewhere, I am going to propose that the audience is those who frequent the Knot Theory and Computing (KT&C) board of the IGKT Forum - i.e. English speaking with an interest focussed on knot form and function.”

Maybe so, but we’ll never know if we don’t make the effort! In the topic called “Knotting Nomenclature – How/What are we talking about?!” (http://igkt.net/sm/index.php?topic=1616.0), a number of people have acknowledged the deficiencies in the traditional knotting terminology. Everyone is free to contribute to a new lexicon which they can be comfortable using.

Great! Where can we find their nomenclature in order to evaluate it?

Dave

39
Great! Where can we find their nomenclature in order to evaluate it?

Mail the chap at this site.
http://jcturner.fortunecity.com/The Braide.htm

I recieved my copy yesterday.

40

I could probably post a PDF file that would be a little on the large size for download. High banders wont have to much of a problem downloading them, but dialup it would take a few days. Let me see what I can come up with for you all over the weekend here. I’ll get back to you all on Monday.

Brian…